Details

Time bar (total: 1.4s)

sample81.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 24.224854%

Guaranteed chance to sample good point: 98.461538%

Results
7.0ms256×body80valid
0.0ms5×body80nan

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
063
163

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 18.3b

Counts
2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) y)
17.1b
(sqrt (+ (* x x) y))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt add-log-exp
3×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
2×add-exp-log flip3-+ sqrt-div add-cbrt-cube flip-+
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log
Counts
2 → 26
Calls
2 calls:
4.0ms
(+ (* x x) y)
4.0ms
(sqrt (+ (* x x) y))

series10.0ms

Counts
2 → 6
Calls
2 calls:
4.0ms
(+ (* x x) y)
6.0ms
(sqrt (+ (* x x) y))

simplify47.0ms

Algorithm
egg-herbie
Counts
32 → 32
Iterations

Useful iterations: 3 (44.0ms)

IterNodesCost
0139151
1485141
21555139
35002138

prune47.0ms

Filtered
25 candidates to 32 candidates (-28.0%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New29332
Fresh000
Picked011
Done000
Total29433

Merged error: 0b

Counts
33 → 4

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b
(* -1/2 (/ y x))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×associate-*r*
10×times-frac
9×add-cube-cbrt *-un-lft-identity
6×add-exp-log add-cbrt-cube
3×pow1 associate-*l*
2×prod-exp cbrt-unprod unswap-sqr
1×cbrt-undiv associate-*r/ div-exp pow-prod-down *-commutative div-inv add-log-exp
Counts
1 → 32
Calls
1 calls:
6.0ms
(* -1/2 (/ y x))

series3.0ms

Counts
1 → 3
Calls
1 calls:
3.0ms
(* -1/2 (/ y x))

simplify61.0ms

Algorithm
egg-herbie
Counts
35 → 35
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0164128
1727118
22950118
35001118

prune36.0ms

Filtered
24 candidates to 35 candidates (-45.8%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New35035
Fresh022
Picked011
Done011
Total35439

Merged error: 0b

Counts
39 → 4

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b
(* 1/2 (/ y x))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×associate-*r*
10×times-frac
9×add-cube-cbrt *-un-lft-identity
6×add-exp-log add-cbrt-cube
3×pow1 associate-*l*
2×prod-exp cbrt-unprod unswap-sqr
1×cbrt-undiv associate-*r/ div-exp pow-prod-down *-commutative div-inv add-log-exp
Counts
1 → 32
Calls
1 calls:
6.0ms
(* 1/2 (/ y x))

series3.0ms

Counts
1 → 3
Calls
1 calls:
3.0ms
(* 1/2 (/ y x))

simplify60.0ms

Algorithm
egg-herbie
Counts
35 → 35
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0164128
1727118
22952118
35001118

prune35.0ms

Filtered
24 candidates to 35 candidates (-45.8%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New35035
Fresh011
Picked011
Done022
Total35439

Merged error: 0b

Counts
39 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

3.8b
(- (* (* x x) (* x x)) (* y y))
14.9b
(sqrt (- (* (* x x) (* x x)) (* y y)))
17.1b
(sqrt (- (* x x) y))
17.2b
(/ (sqrt (- (* (* x x) (* x x)) (* y y))) (sqrt (- (* x x) y)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
49×add-sqr-sqrt times-frac
38×add-cube-cbrt *-un-lft-identity
19×difference-of-squares
8×sqrt-div
7×associate-/r* associate-/l*
6×pow1 add-exp-log add-cbrt-cube add-log-exp
5×flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ associate-/l/
1×cbrt-undiv sub-neg sqrt-undiv frac-2neg diff-log div-exp clear-num div-inv
Counts
4 → 125
Calls
4 calls:
9.0ms
(- (* (* x x) (* x x)) (* y y))
9.0ms
(sqrt (- (* (* x x) (* x x)) (* y y)))
4.0ms
(sqrt (- (* x x) y))
16.0ms
(/ (sqrt (- (* (* x x) (* x x)) (* y y))) (sqrt (- (* x x) y)))

series33.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(- (* (* x x) (* x x)) (* y y))
9.0ms
(sqrt (- (* (* x x) (* x x)) (* y y)))
6.0ms
(sqrt (- (* x x) y))
11.0ms
(/ (sqrt (- (* (* x x) (* x x)) (* y y))) (sqrt (- (* x x) y)))

simplify51.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03481804
113481685
250011649

prune108.0ms

Filtered
93 candidates to 137 candidates (-47.3%)
Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New1370137
Fresh000
Picked011
Done033
Total1374141

Merged error: 0b

Counts
141 → 4

regimes255.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 21.2b

bsearch29.0ms

Steps
ItersRangePoint
7
4.1911267630183946e+96
1.3995492908524915e+98
1.0994862274100045e+98
9
-3.2320814797367493e+162
-4.798664768876341e+153
-1.3525718991927634e+154

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0229
1229

end0.0ms

sample487.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 24.224854%

Guaranteed chance to sample good point: 98.461538%

Results
216.0ms8000×body80valid
2.0ms89×body80nan

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